<span>Угловой коэффициент касательной, проведенной к графику функции y=f(x) в точке с абсциссой x0, равен производной функции в этой точке.
а) f(x) = (1/2)x</span>²+3x+2, xo = 1.
f'(x) = x+3,
f'(xo) = 1+3 = 4.
б) f(x) = 2sin 2x, xo = π/3.
<span>f'(x) = 4cos 2x,
</span> f'(xo) = 4 *cos(2π/3) = 4*(-1/2) = -2<span>.
</span>
в) f(x) = √(3x-8), xo = 3.
f'(x) = 3/(2√(3x-8)),
f'(xo) = 3/(2√(3*3-8)) = 3/2 = 1,5.
<span>г) </span>
![f(x)=(2x-4)^{ \frac{3}{4} }.](https://tex.z-dn.net/?f=f%28x%29%3D%282x-4%29%5E%7B+%5Cfrac%7B3%7D%7B4%7D+%7D.)
xo = 10.
![f'(x_o)= \frac{3}{2 \sqrt[4]{2*10-4} } = \frac{3}{2* \sqrt[4]{16} } = \frac{3}{4} =0,75.](https://tex.z-dn.net/?f=f%27%28x_o%29%3D+%5Cfrac%7B3%7D%7B2+%5Csqrt%5B4%5D%7B2%2A10-4%7D+%7D+%3D+%5Cfrac%7B3%7D%7B2%2A+%5Csqrt%5B4%5D%7B16%7D+%7D+%3D+%5Cfrac%7B3%7D%7B4%7D+%3D0%2C75.)